The problem with the "simple formula" is that it's a truism. Yeah of course if you expend more energy than you use you lose weight. That humans don't violate the laws of thermodynamics is hardly shocking.The real challenge is actually causing the human body to use more energy than it expends over a sustained period.

Neither exercise nor calorie restriction has a proven track record of being able to do this. Even the most favourable studies done on the effectiveness of such regimes show that we're talking at most a 5% success rate (and some studies put it much lower than that, in the sub 1% range).